This project is intended to increase our understanding of the use and application of mathematical and statistical models in toxicology and biochemistry and to implement new mathematical models to aid in explaining current research findings. The research effort explores a diverse range of biological areas, including carcinogenesis, pharmacology, developmental biology, neurology and immunology. Major accomplishments include (1) used available modeling constructs ranging from simple to highly complex to determine if data needs to be obtained on the toxicokinetics of compounds being considered for NTP chronic bioassays and, when necessary, aided in the design of these toxicokinetic studies (2) methods were derived for the analysis of data on premalignant lesions and carcinomas simultaneously (3) a stochastic model of carcinogenesis which account for intercellular communication was developed and is currently being studied (4) methods were developed for linking PBPK models, premalignant lesion data, cell labelling data and tumor incidence data simultaneously and then were applied to two chemicals (5) used the models and methods developed in the laboratory to give direction to improvements in environmental risk assessment (6) an earlier physiological model of dioxin disposition was modified by including distribution of blood among major vessels and capillary spaces and by adding representation of the complex biochemical mechanisms responsible for TCDD's effects on thyroid hormones in the blood (7) a complete mechanistic model for liver carcinogenesis in female rats following TCDD exposure was developed using all available biochemical, premalignant lesion, malignancy and cell labeling data (8) built and experimentally validated a mathematical model describing the specific phases of the cell cycle.